# Roll me a prime

**Discrete Mathematics**Level 5

Optimus Prime loves prime numbers. So, he decides to keep rolling a fair six-sided die, until he rolls a prime number less than 100. e.g. If his last two rolls were a 6 and then a 1, he would be done since 61 is a prime number. Or, for example, any time he rolls a 3 he would also be done since 3 is a prime number.

If the expected number of rolls he must make is \(\dfrac{a}{b}\), where \(a\) and \(b\) are coprime positive integers, what is \(a+b\)?